Column experiments were conducted in an airlift reactor containing a certain amount of crosslinked chitosan–iron(III) (Ch-Fe), to examine the effects of adsorbent mass, flow rate, and influent concentrations on Cr(VI) removal. The breakthrough time increased with an increase in Ch-Fe mass, but decreased with an increase in initial Cr(VI) concentration. The exhaustion time decreased with an increase in initial Cr(VI) concentration. The capacity at the breakthrough point increased with an increase in Ch-Fe mass, flow rate, and initial Cr(VI) concentration. The capacity at the exhaustion point increased with an increase in flow rate, but showed no specific trend with an increase in initial Cr(VI) concentration. The bed volumes at breakthrough point increased with an increase in Ch-Fe, flow rate and Cr(VI) concentration. The adsorbent exhaustion decreased with an increase in flow rate and Ch-Fe, but increased with an increase in initial Cr(VI) concentration. Columns with large amounts of Ch-Fe are preferable for obtaining optimal results during the adsorption process. The higher the flow velocity, the better the column performance. The Thomas, Clark and Yoon–Nelson models were applied to the experimental results. Good agreement was observed between the predicted theoretical breakthrough curves and the experimental results.

INTRODUCTION

With industrialization, more and more chromium is being used in industrial activities, such as electroplating and metal finishing processes, leather tanning, pigments, and the chemical industry. Chromium exists in trivalent (Cr(III)) and hexavalent (Cr(VI)) states. The hexavalent form is considered more hazardous to public health due to its mutagenic and carcinogenic properties. The maximum permissible levels of Cr(VI) in drinking and industrial wastewater were set by the US Environmental Protection Agency (EPA) as 0.05 mg L−1 and 0.20 mg L−1, respectively (Miretzkya & Cirelli 2010). However, the search for an effective treatment of the industrial wastewater is growing, and is very important for a healthy environment in general. Therefore chromium was placed at the top of the priority list of toxic pollutants by the US EPA (Liu et al. 2006).

Chemical reduction to Cr(III) followed by precipitation under alkaline conditions, as well as ion exchange, electrochemical precipitation and reverse osmosis, are the conventional methods used to remove Cr(VI) from industrial wastewater. These methods require large amounts of chemicals and energy, and generate toxic sludge or other residues that are difficult to manage and treat (Şahin & Öztürk 2005). Therefore, it is important to develop safer, low-cost, environmentally friendly methods for removing Cr(VI) from wastewater. Adsorption is a good option, and is one of the most economically favorable and technically easy methods. A variety of materials have been used as Cr(VI) adsorbents, including sugarcane bagasse waste biomass (Ullah et al. 2013), sulfate-crosslinked chitosan (Kahu et al. 2014), activated carbon (Zinicovscaia et al. 2014), Peganum harmala seed (Khosravi et al. 2014), chitosan–iron crosslinked complex (Zimmermann et al. 2010), and magnetic chitosan–iron(III) hydrogel (Yu et al. 2013).

The process of adsorption has been carried out mostly in fixed and moving beds. However, operational complexity and the limitation of the efficiency of removal in a fixed bed have led to a search for new and efficient equipment that can improve removal efficiency without additional mechanical complications (Mohantya et al. 2008). Air-lift reactors, in their various forms and manifestations, belong to the category of moving beds in which compressed air is used to simultaneously aerate and agitate the liquid with controlled recirculation. Thus, simultaneous gas–liquid (or gas–liquid–solid) mixing and liquid recirculation is achieved using only compressed air. Air-lift reactors can, therefore, provide a very important contacting system for the liquid phase adsorption of pollutants, due to their basic advantages, such as a simple construction without moving parts, a high liquid phase content, an excellent heat transfer capacity, a reasonable interphase mass transfer, and good mixing properties at low energy consumption, as the gas phase serves the dual function of aeration and agitation (Chisti 1989).

Air-lift-type reactors have been used for the removal of textile dye Black 8, Brilliant Orange 3R, Scarlet R and Black DN using chitosan and modified chitin as adsorbents (Filipkowska 2008; Filipkowska & Waraksa 2008). Recently, this reactor has been used to remove Mn, Zn and Cr heavy metals, using a natural zeolite clinoptilolite (Stylianou et al. 2015), and cadmium by activated sludge (Filipkowska et al. 2015).

Previous investigations demonstrated that chitosan–Fe(III) crosslinked complex (Ch-Fe) has good adsorption capacity for Cr(VI) in batch method (Zimmermann et al. 2010) and fixed bed (Demarchi et al. 2015). Based on those results, this study investigates the capacity of Ch-Fe adsorption capacity using a different method: moving bed, through an air-lift reactor, in order to compare maximum absorption capacity obtained by other methods. For this purpose, the Cr(VI) adsorption capacity of the adsorbent was investigated as a function of different operating conditions, such as flow rate, initial Cr(VI) concentration, and amount of adsorbent. The experimental data were used in three different kinetic models to find the best fit.

EXPERIMENTAL

Materials

The procedure for the preparation and characterization of the Ch-Fe was the same as that reported in the literature (Santos et al. 2011). The quantity of iron in the sample (80.6 mg g−1) was determined by colorimetric methods using 1.0-phenantroline and a Spectrovision DB 2500 spectrophotometer (Standard Methods for the Examination of Water and Wastewater 1998). The zero-point charge (pHzpc) 8.9 was determined using a potentiometric titration. All the reagents used in this study were of analytical grade. An aqueous solution of Cr(VI) was prepared by dissolving K2Cr2O7 (VETEC, São Paulo, Brazil) in distilled water. A stock solution with a concentration of 1,000 mg L−1 of K2CrO4 was prepared and subsequently diluted.

Adsorption study

The air-lift-type reactor (Figure 1) was built of glass, with the following dimensions:internal diameter of 1.25 cm, height of 25 cm, and internal volume of 55 mL, with internal projections to alter the itinerary of the liquid and increase the movement of the particles in its interior (Filipkowska 2008). The flow rate was controlled with a peristaltic pump, Spectrovision model PP2. Aeration was applied at a pressure of 5 psi, to force Ch-Fe movement in the reactor, through a Fanem compress pump (model Diapump). With this system, the adsorption studies were carried out by changing the following parameters; amount of adsorbent (100, 150, 200, 250 and 500 mg), flow rate (2.0, 5.0 and 10.0 mL min−1), and concentration of the Cr(VI) solution (40, 75 and 150 mg L−1). The Cr(VI) solutions were maintained at pH 2.0 (Zimmermann et al. 2010).
Figure 1

The schematic diagram of the air-lift-type reactor.

Figure 1

The schematic diagram of the air-lift-type reactor.

Determination of Cr(VI) concentration in the air-lift reactor

The desired breakthrough volume (VB) was determined at 5% of the influent Cr(VI) concentration. The flow through the tested column was continued until the Cr(VI) concentration of column effluent approached 90% of initial influent concentration, which indicated the exhaustion volume (VE). The efficiency of the process was calculated by monitoring the reducing the Cr(VI) concentration after passing through the reactor, comparing the concentration of the solution in the inlet and outlet of the system. Samples were taken at regular time intervals. The residual Cr(VI) concentration was measured using a double beam UV–visible spectrophotometer (Spectrovision model DB 188S, China) at 540 nm, using diphenylcarbazide as the complexing agent (Standard Methods for the Examination of Water and Wastewater 1998).

Models used

The loading behavior of Cr(VI) to be adsorbed from solution in a dynamic system, such as an air-lift reactor, is usually expressed by the terms Ct (effluent chromium concentration) and C0 (influent chromium concentration), as a function of elution time or volume of the effluent, for a given amount of adsorbent, giving a breakthrough curve (Malkoc & Nuhoglu 2006). Thus, the adsorption capacity, qt (mg g−1), was determined according to the equation 
formula
1
where V (L) is the volume of solution, C0 (mg L−1) is the influent concentration, Ct (mg L−1) is the effluent concentration, and m (g) is the amount of Ch-Fe.

Thomas model

The Thomas model is one of the most general and widely used models in column performance theory. It is based on the assumption that the process follows Langmuir kinetics with no axial dispersion. The Thomas model has the following form: 
formula
2
where Q is the flow rate (mL min−1), x is the adsorbent mass (g). The maximum adsorption capacity qe (mg g−1) and the velocity constant KTh (mL mg−1 min−1) can be determined from a plot of Ct/C0 against t for a given flow rate using nonlinear regression analysis (Thomas 1944).

Yoon–Nelson model

Another model that is easy to use is the Yoon–Nelson model, which is based on the assumption that the rate of decrease in probability of adsorption for each adsorbate molecule is proportional to the probability of adsorbate adsorption and the probability of adsorbate breakthrough on the adsorbent. The Yoon–Nelson equation for a single component system is expressed as: 
formula
3
where kYN is the rate constant (L min−1) and τ is the time required for adsorbate breakthrough. The approach involves a plot of Ct/(C0Ct) against t according to Equation (3). The parameters of kYN and τ can be obtained using the nonlinear regressive method (Yoon & Nelson 1985).

Clark model

The Clark model introduces a new procedure to simulate the breakthrough curve using the Freundlich isotherm constant. The Clark equation is expressed as: 
formula
4
where n is the Freundlich adsorption constant, A is the constant Clark model, and r is the adsorption rate (mg L−1 min−1). The values of A and r can be obtained from a plot of Ct/C0 against t at a given amount of adsorbent and flow rate, using nonlinear regressive analysis, (Clark 1987).

Error analysis

To find out the best applicable model from the goodness of fit with the experimental values, a number of error analysis methods, such as χ2 analysis and the sum of squares for error (SSE), were used in the present study to find out the model that best fits the experimental observation. The expression for χ2 analysis is 
formula
5
where ye is the experimental data and yc is the calculated data from equation used. If the data from the model are similar to the experimental data, χ2 will be a small number; however, if they are different, χ2 will be a larger number.
The SSE values were calculated by the equation 
formula
6
where ye is the experimental data and yc is the calculated data from equation used. The above statistical error expressions were applied to all breakthrough curves of the model equations.

RESULTS AND DISCUSSION

Effect of initial Cr(VI) concentration

Initial Cr(VI) concentrations of 40, 75 and 150 mg L−1 were used to study the column studies at flow rate of 5 mL min−1 and 250 mg of adsorbent. The effect of initial Cr(VI) concentration on breakthrough curves is shown in Figure 2. Analysis of the breakthrough curves reveals that the increase in concentration of the solution results in a decrease of the values of breakthrough volume (VB) and exhaustion volume (VE). The reason for this behavior is the saturation of the adsorption sites of the Ch-Fe. As the concentration of Cr(VI) increases, the amount of ions that reaches the adsorption site also increases, and consequently, the sites are occupied more quickly. On the other hand, the amount of Cr(VI) adsorbed at the exhaustion column (qE) and the amount of Cr(VI) adsorbed at the breakthrough column (qB) was increased with initial Cr(VI) concentration, which was expected, as more adsorption occurs at a higher initial Cr(VI) concentration. The main effect of adsorption capacity is higher when the chromium concentration is increased, as shown in Table 1.
Table 1

Column data and parameters obtained at different initial Cr(VI) ion concentrations (C0), amount of Ch-Fe (m) and flow rates

  VB (mL) VE (mL) TB (min) TE (min) qB (mg) qE (mg) qt (mg g−1
C0 (mg L−1(m= 250 mg; flow rate 5 mL min−1
40 220 415 44 83 7.6 11.0 44.0 
75 150 255 30  51 9.7 18.2 72.8 
150 80 380 16 70 12.3 30.0 120.0 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 55 245 11 60 4.0 10.2 102.0 
150 120 475 24 95 9.3 16.9 112.7 
200 135 465 30 93 12.8 17.5 87.5 
250 150 255 32 51 9.7 18.2 72.8 
500 320 1075 64 215 24.0 38.6 137.2 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
2.0 155 275 77.5 195 11.3 15.1 60.4 
5.0 150 255 32 51 9.7 18.4 72.8 
10.0 55 305 5.5 37 6.1 11.0 44.0 
  VB (mL) VE (mL) TB (min) TE (min) qB (mg) qE (mg) qt (mg g−1
C0 (mg L−1(m= 250 mg; flow rate 5 mL min−1
40 220 415 44 83 7.6 11.0 44.0 
75 150 255 30  51 9.7 18.2 72.8 
150 80 380 16 70 12.3 30.0 120.0 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 55 245 11 60 4.0 10.2 102.0 
150 120 475 24 95 9.3 16.9 112.7 
200 135 465 30 93 12.8 17.5 87.5 
250 150 255 32 51 9.7 18.2 72.8 
500 320 1075 64 215 24.0 38.6 137.2 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
2.0 155 275 77.5 195 11.3 15.1 60.4 
5.0 150 255 32 51 9.7 18.4 72.8 
10.0 55 305 5.5 37 6.1 11.0 44.0 
Figure 2

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different initial concentration of Cr(VI); flow rate 5.0 mL min−1; amount of Ch-Fe 250 mg. Lines represent VB (Ct/C0 = 5%) and VE (Ct/C0 = 95%), respectively.

Figure 2

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different initial concentration of Cr(VI); flow rate 5.0 mL min−1; amount of Ch-Fe 250 mg. Lines represent VB (Ct/C0 = 5%) and VE (Ct/C0 = 95%), respectively.

The adsorption capacity was therefore expected to increase with the increase in influent concentration because a high concentration difference provides a high driving force for the adsorption process (Zou et al. 2013). Similar behavior was reported for the adsorption of Cr(VI) by other biosorbents: cyanobacterial (Kiran & Kaushik 2008), thermally activated weed Salvinia cucullata (Baral et al. 2009), and waste tea (Malkoc & Nuhoglu 2006).

Effect of amount of CH-Fe

The breakthrough curves for various adsorbent amounts (100, 150, 200, 250 and 500 mg) at a constant flow rate of 5 mL min−1 and Cr(VI) initial concentration of 75 mg L−1 are shown in Figure 3. Comparing the curves in Figure 3 and observing the values of VB and VE in Table 1, it is observed that the amount of Ch-Fe is fundamental in the process of adsorption. Also, the values of VB, VE, breakthrough time (TB) and exhaustion volume (TE) increase as Ch-Fe increased. This result is due to the increase in the amount of adsorption sites (Fe3+). The qB rises when the amount of Ch-Fe increases from 4 to 24 mg, while the amount of adsorbent ranges from 100 to 500 mg.
Figure 3

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different amount of Ch-Fe: initial concentration Cr(VI) 75 mg L−1; flow rate 5.0 mL min−1. Lines represent VB (Ct/C0 = 5%) and VE (v = 95%), respectively.

Figure 3

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different amount of Ch-Fe: initial concentration Cr(VI) 75 mg L−1; flow rate 5.0 mL min−1. Lines represent VB (Ct/C0 = 5%) and VE (v = 95%), respectively.

High adsorption capacity was observed at the highest Ch-Fe amount due to an increase in the surface of the adsorbent, which provided more binding sites for the adsorption (Fe3+). The adsorption capacities are listed in Table 1. However, qE does not increase in proportion to the adsorption sites, showing that some of the adsorption sites are not accessible to the Cr(VI). This same relationship was observed in the processes of adsorption of Cr(VI) by Ch-Fe in the bath system (Zimmermann et al. 2010). Similar behaviors for the adsorption process of other adsorbents and adsorbate have been reported in some of the previous studies (Filipkowska et al. 2015; Loredo-Cancino et al. 2015).

Effect of the solution flow rate

The effect of flow rate on the adsorption of Cr(VI) in the Ch-Fe was investigated by changing the flow rate from 2 to 10 mL min−1. In this process, the initial adsorbate concentrations and the amount of Ch-Fe were maintained at 75 mg L−1 and 250 mg, respectively. The effect of flow rate on breakthrough performance at the above operating conditions is shown in Table 1. Breakthrough curves for three flow rates are shown in Figure 4.
Figure 4

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different flow rates: initial concentration Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg. Lines represent VB (Ct/C0 = 5%) and VE (Ct/C0 = 95%), respectively.

Figure 4

Breakthrough curve for Cr(VI) adsorption by CH-Fe at different flow rates: initial concentration Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg. Lines represent VB (Ct/C0 = 5%) and VE (Ct/C0 = 95%), respectively.

The results show that VB and TB decrease significantly when the flow rate increases. This trend was in agreement with other research (Zou et al. 2013). However, the qt is not greatly influenced, since the amount of adsorbent is the same; therefore, there is the same amount of adsorption sites. The value of qB was greatly diminished when the flow rate was increased from 2 to 10 mL min−1. At a higher flow rate, the adsorption capacity was lower due to insufficient contact time of the Cr(VI) in the reactor and diffusion of the solute into the pores of the adsorbent; therefore, the solute left the reactor before equilibrium occurred. This behavior shows that the adsorption of the Cr(VI) is slow, and the increased flow rate does not allow these ions to reach the adsorption site. In addition, when the flow rate is high, the leaching process occurs simultaneously with the adsorption process, resulting in the decrease of adsorption of Cr(VI), decreasing the value of qt.

The maximum adsorption capacity of Cr(VI) by the Ch-Fe, using the air-lift-type reactor (72.8 mg g−1), is higher than its corresponding adsorption capacity in a fixed-bed column (50.4 mg g−1) at the same experimental conditions (Demarchi et al. 2015). This behavior can be attributed to the process of agitation, allowing greater contact time between the adsorbent and the adsorbate, in the air-lift-type reactor, compared to the fixed-bed column.

Modeling and analysis of column data

Thomas model

Recently this model was used in studies with reactors of air-lift type (Filipkowska et al. 2015). The column data were fitted to the Thomas model to determine the Thomas rate constant (KTh) and maximum adsorption capacity (qe). A non-linear regression analysis of Equation (2) was used to evaluate the Thomas model. The comparison of the experimental and predicted breakthrough curves obtained at different flow rates with 250 mg of Ch-Fe and Cr(VI) solution of 75 mg L−1, according to the Thomas model, is shown in Figure 5. The calculated Thomas model parameters with different conditions of concentration of Cr(VI), amount of adsorbent, and flow rates are listed in Table 2.
Table 2

Thomas model constants at different initial Cr(VI) ion concentrations (C0), flow rates and amount of Ch-Fe (m)

  KTh (mL mg−1min−1qc (mg g−1R2 SSE χ2 qexp (mg g−1
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 4.1 44.0 0.9956 4.6 × 10−3 9.2 × 10−4 44.0 
75 2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.7 
150 0.7 120.0 0.9956 4.6 × 10−3 9.2 × 10−4 83.7 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
1.5 60.4 0.9948 8.6 × 10−3 8.6 × 10−4 60.0 
2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.5 
10 4.8 44.0 0.9844 2.6 × 10−2 3.7 × 10−3 44.0 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 1.6 102.0 0.8352 9.8 × 10−2 1.2 × 10−2 101.5 
150 1.3 112.7 0.8769 0.24731 1.4 × 10−2 113.2 
200 1.5 87.5 0.9881 5.6 × 10−2 3.5 × 10−3 87.3 
250 2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.5 
500 0.5 137.2 0.9103 0.27236 1.2 × 10−2 77.3 
  KTh (mL mg−1min−1qc (mg g−1R2 SSE χ2 qexp (mg g−1
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 4.1 44.0 0.9956 4.6 × 10−3 9.2 × 10−4 44.0 
75 2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.7 
150 0.7 120.0 0.9956 4.6 × 10−3 9.2 × 10−4 83.7 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
1.5 60.4 0.9948 8.6 × 10−3 8.6 × 10−4 60.0 
2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.5 
10 4.8 44.0 0.9844 2.6 × 10−2 3.7 × 10−3 44.0 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 1.6 102.0 0.8352 9.8 × 10−2 1.2 × 10−2 101.5 
150 1.3 112.7 0.8769 0.24731 1.4 × 10−2 113.2 
200 1.5 87.5 0.9881 5.6 × 10−2 3.5 × 10−3 87.3 
250 2.1 72.8 0.9869 1.4 × 10−2 1.2 × 10−3 45.5 
500 0.5 137.2 0.9103 0.27236 1.2 × 10−2 77.3 
Figure 5

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Thomas model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

Figure 5

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Thomas model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

It is observed that there is similarity between the calculated and experimental data points, which suggests that the Thomas model fits the experimental breakthrough curves satisfactorily.

As shown in Table 2, the KTh values decrease and qe values increase, with an increase in both the adsorbent mass and initial Cr(VI) concentration. The decrease in KTh reflects the increasing resistance to mass transport, as a result of an increase in the adsorbent mass. Table 2 shows that the increase in flow rate causes a decrease in the qe and increase in KTh. Also, the KTh values increase with higher flow rates, which may be due to a decrease in importance of mass transport resistance. The decrease of qe with increment of flow rate is clear, since adsorption capacity is dependent on the contact time between the adsorbent and the Cr(VI) ion.

The statistic parameter (R2, SSE and χ2) for the nonlinear regression analysis, shown in Table 2, is acceptable, showing good agreement of the Thomas model with the experimental data.

Yoon–Nelson model

The theoretical model of Yoon–Nelson, Equation (3), was applied to investigate the breakthrough behavior of Cr(VI) on Ch-Fe. A non-linear regression analysis of the Yoon–Nelson equation was used, and the results of the experimental data and model-calculated curve are shown in Figure 6. The values of kYN (a rate constant) and τ (the time required for 50% Cr(VI) breakthrough) could be obtained, and the values are listed in Table 3. The time required for 50% breakthrough increased with the amount of adsorbent, from 42.6 to 187 min, when the amount of the Ch-Fe increased from 100 to 500 mg. It is observed that the values of kYN decreased, with an increase in the amount of Ch-Fe. Moreover, the values of kYN are found to increase with an increment in both initial concentrations and flow rates, whereas a reverse trend is observed for the values of τ. The data shown in Table 3 indicate that the values of τ obtained are very similar to the experimental values of τexp.
Table 3

Yoon–Nelson model constants at different initial Cr(VI) ion concentrations (C0), flow rates and amount of Ch-Fe (m)

  kYN (L min−1τ (min) R2 SSE χ2 τexp (min) 
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 0.174 66 0.9986 0.404 0.0809 61 
75 0.039 205 0.9659 0.632 0.0632 41 
150 0.082 37 0.9979 1.068 0.0971 31 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
0.221 112 0.9970 489.2 48.9251 105 
0.039 205 0.9659 0.632 0.0632 41 
10 0.257 20 0.9881 0.136 0.0341 21 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 0.100 29 0.9343 3.1 0.5178 35 
150 0.028 24 0.8663 10.7 0.8931 36 
200 0.069 29 0.9321 501.1 41.7629 41 
250 0.039 205 0.9659 0.632 0.0632 41 
500 0.036 107 0.7246 695.8 40.9347 87 
  kYN (L min−1τ (min) R2 SSE χ2 τexp (min) 
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 0.174 66 0.9986 0.404 0.0809 61 
75 0.039 205 0.9659 0.632 0.0632 41 
150 0.082 37 0.9979 1.068 0.0971 31 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
0.221 112 0.9970 489.2 48.9251 105 
0.039 205 0.9659 0.632 0.0632 41 
10 0.257 20 0.9881 0.136 0.0341 21 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 0.100 29 0.9343 3.1 0.5178 35 
150 0.028 24 0.8663 10.7 0.8931 36 
200 0.069 29 0.9321 501.1 41.7629 41 
250 0.039 205 0.9659 0.632 0.0632 41 
500 0.036 107 0.7246 695.8 40.9347 87 
Figure 6

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Yoon–Nelson model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

Figure 6

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Yoon–Nelson model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

The statistical parameters (R2, SSE and χ2) for the nonlinear regression analyses are satisfactory for most conditions analyzed, showing effective correlation between experimental and theoretical data, with the exception of the change in the amount of the absorbent, where the parameters R2, SSE and χ2 have unsatisfactory values.

Clark model

In a previous batch equilibrium study (Zimmermann et al. 2010), it was found that the Freundlich model fits the adsorption of Cr(VI) by crosslinked chitosan–iron. Therefore, the Freundlich constant n was used to calculate the parameters in the Clark model. The values of A and r in the Clark model, Equation (4), were determined using non-linear regression analysis. As shown in Table 4, as both flow rate and initial chromium concentration decreased, the values of r increased. However, the values of r increased when the amount Ch-Fe adsorbent increased. Figure 7 shows the experimental and theoretical values of the breakthrough curve obtained under flow rates. It appears that the simulation of the whole breakthrough curve is effective with the Clark model.
Table 4

Clark model constants at initial Cr(VI) ion concentrations (C0), flow rates and amount of Ch-Fe (m)

  A r (L min−1n R2 SSE χ2 
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 691614 0.2226 2.1 0.9959 1.7 × 10−3 4.1 × 10−4 
75 414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
150 111 0.1382 2.0 0.9958 6.2 × 10−2 6.4 × 10−3 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
112580 0.0747 2.0 0.9952 8.5 × 10−3 8.6 × 10−4 
414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
10 1820 0.3595 1.9 0.9891 1.3 × 10−2 2.8 × 10−3 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 61.8 0.1510 2.2 0.9893 6.4 × 10−3 1.3 × 10−3 
150 1601 0.2136 2.2 0.9805 3.3 × 10−2 2.7 × 10−3 
200 312 0.1244 2.2 0.9824 4.4 × 10−2 3.4 × 10−3 
250 414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
500 291 0.0637 2.2 0.9585 1.8 × 10−2 2.3 × 10−1 
  A r (L min−1n R2 SSE χ2 
C0 (mg L−1(m = 250 mg; flow rate 5 mL min−1
40 691614 0.2226 2.1 0.9959 1.7 × 10−3 4.1 × 10−4 
75 414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
150 111 0.1382 2.0 0.9958 6.2 × 10−2 6.4 × 10−3 
Flow rate (mL min−1(m = 250 mg; C0 = 75 mg L−1
112580 0.0747 2.0 0.9952 8.5 × 10−3 8.6 × 10−4 
414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
10 1820 0.3595 1.9 0.9891 1.3 × 10−2 2.8 × 10−3 
m (mg) (Flow rate 5 mL min−1; C0 = 75 mg L−1
100 61.8 0.1510 2.2 0.9893 6.4 × 10−3 1.3 × 10−3 
150 1601 0.2136 2.2 0.9805 3.3 × 10−2 2.7 × 10−3 
200 312 0.1244 2.2 0.9824 4.4 × 10−2 3.4 × 10−3 
250 414 0.1419 1.8 0.9869 1.7 × 10−2 1.9 × 10−3 
500 291 0.0637 2.2 0.9585 1.8 × 10−2 2.3 × 10−1 
Figure 7

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Clark model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

Figure 7

Comparison of the experimental and predicted breakthrough curves obtained at different flow rates according to the Clark model: Cr(VI) 75 mg L−1; amount of Ch-Fe 250 mg.

The results indicated that they were all acceptable fits, with coefficient correlations (R2) ranging from 0.9585 to 0.9958 with values of SSE less than 0.23 and χ2 less than 0.01. Subsequently, the correlation of Ct/C0 and time according to Equation (4) is significant.

Among the Thomas, Yoon–Nelson, and Clark models, the values of R2 from the Clark model and the Thomas model are higher than those of the Yoon–Nelson model. The SSE and χ2 for the Yoon–Nelson was the highest of all the experimental conditions, and the lowest for the Clark and Thomas models. In all the conditions examined, the predicted breakthrough curves from the Clark and Thomas models showed reasonably better agreement with the experimental curves than the Yoon–Nelson model. Thus, it was concluded that the Thomas and Clark models were better for predicting Cr(VI) adsorption by Ch-Fe in an air-lift reactor than the Yoon–Nelson model.

CONCLUSION

The results indicate that the increase in flow rate decreases the VB. The maximum adsorption capacity of Cr(VI) increases with the increase in the initial Cr(VI) concentration. The Clark, Thomas and Yoon–Nelson models for Ch-Fe on Cr(VI) adsorption were used to predict the breakthrough curves under variable experimental conditions. All the models fit the experimental data very well. Due to ready availability and high efficiency of removal of Cr(VI), with maximum adsorption capacity of 182.9 mg g−1, Ch-Fe is a very good adsorbent for removing Cr(VI) from aqueous solutions using the fluidized bed method.

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